Generalised short-time Hartley transforms for speech processing

Abstract

This paper addresses the problem of reducing the complexity involved in computing large discrete Hartley transforms with N-1 degrees of freedom, by first computing short-time transforms with M samples (M>N) and then using this to compute the full transform of length N samples. We present a solution to the problem as it relates to discrete Hartley transforms (DHTs). Short-time Hartley transforms are derived and simplified in terms of type-I DHTs for which efficient fast algorithms exist. We also give further simplifications of type-IV in terms of type-II, and type-III in terms of type-I DHTs.<>